lovefederer2
title 'Crime Rates per 100,000 Population by State';
input State $1-15 Murder Rape Robbery Assault
Burglary Larceny Auto_Theft;
cards;
Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7
Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3
Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5
Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4
California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
Colorado 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1
Connecticut 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2
Delaware 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0
Florida 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4
Georgia 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9
Hawaii 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4
Idaho 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6
Illinois 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6
Indiana 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4
Iowa 2.3 10.6 41.2 89.8 812.5 2685.1 219.9
Kansas 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3
Kentucky 10.1 19.1 81.1 123.3 872.2 1662.1 245.4
Louisiana 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7
Maine 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9
Maryland 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5
Massachusetts 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1
Michigan 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5
Minnesota 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1
Mississippi 14.3 19.6 65.7 189.1 915.6 1239.9 144.4
Missouri 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4
Montana 5.4 16.7 39.2 156.8 804.9 2773.2 309.2
Nebraska 3.9 18.1 64.7 112.7 760.0 2316.1 249.1
Nevada 15.8 49.1 323.1 355.0 2453.1 4212.6 559.2
New Hampshire 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4
New Jersey 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5
New Mexico 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5
New York 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8
North Carolina 10.6 17.0 61.3 318.3 1154.1 2037.8 192.1
North Dakota 0.9 9.0 13.3 43.8 446.1 1843.0 144.7
Ohio 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4
Oklahoma 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8
Oregon 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9
Pennsylvania 5.6 19.0 130.3 128.0 877.5 1624.1 333.2
Rhode Island 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4
South Carolina 11.9 33.0 105.9 485.3 1613.6 2342.4 245.1
South Dakota 2.0 13.5 17.9 155.7 570.5 1704.4 147.5
Tennessee 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0
Texas 13.3 33.8 152.4 208.2 1603.1 2988.7 397.6
Utah 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5
Vermont 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2
Virginia 9.0 23.3 92.1 165.7 986.2 2521.2 226.7
Washington 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3
West Virginia 6.0 13.2 42.2 90.9 597.4 1341.7 163.3
Wisconsin 2.8 12.9 52.2 63.7 846.9 2614.2 220.7
Wyoming 5.4 21.9 39.7 173.9 811.6 2772.2 282.0
;
proc princomp out=Crime_Components;
run;
想得出有关犯罪的回归方程……
弱问一句,SAS里直接实现主成分回归分析的语句吗?
zxcv_bnm
运行得
看累计贡献率>=85%即可
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 6.52720703 5.06230750 0.6527 0.6527
2 1.46489954 0.45700617 0.1465 0.7992
3 1.00789337 0.00789330 0.1008 0.9000
4 1.00000006 1.00000006 0.1000 1.0000
5 0.00000000 0.00000000 0.0000 1.0000
6 0.00000000 0.00000000 0.0000 1.0000
7 0.00000000 0.00000000 0.0000 1.0000
8 0.00000000 0.00000000 0.0000 1.0000
9 0.00000000 0.00000000 0.0000 1.0000
10 0.00000000 0.00000000 0.0000 1.0000
11 0.00000000 0.00000000 0.0000 1.0000
12 0.00000000 0.0000 1.0000
Eigenvectors
Prin1 Prin2 Prin3 Prin4 Prin5 Prin6
n 0.377758 0.207491 -.073814 0.00000 0.00000 0.00000
a 0.385380 -.144368 0.007914 -0.00007 0.00000 0.00000
j 0.385380 -.144368 0.007914 -0.00007 0.00000 0.00000
sumj 0.385380 -.144368 0.007914 -0.00007 0.00000 0.00000
x 0.331876 0.436377 0.045974 -0.00000 0.00000 0.00000
ak 0.385227 -.146136 0.009025 0.00022 0.00000 0.00000
Prin1 0.391414 0.000000 0.000000 0.00000 0.00000 0.00000
Prin2 0.000000 0.826221 0.000000 -0.00000 0.00000 0.00000
Prin3 0.000000 0.000000 0.996077 -0.00000 0.00000 0.00000
Prin4 -.000000 0.000000 0.000000 1.00000 0.00000 0.00000
Prin5 0.000000 0.000000 0.000000 0.00000 1.00000 0.00000
Prin6 0.000000 0.000000 0.000000 0.00000 0.00000 1.00000
conapika
由于数据单位不同,故将其标准化后在进行主成分分析;此外,我们会发现前三个主成分的累计方差贡献率>85%(从下面结果看出),所以又对前三个主成分对样本进行分数排名.具体如下:
程序:
data Crime;
input State $1-15 Murder Rape Robbery Assault
Burglary Larceny Auto_Theft;
cards;
Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7
Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3
Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5
Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4
California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
Colorado 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1
Connecticut 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2
Delaware 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0
Florida 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4
Georgia 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9
Hawaii 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4
Idaho 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6
Illinois 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6
Indiana 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4
Iowa 2.3 10.6 41.2 89.8 812.5 2685.1 219.9
Kansas 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3
Kentucky 10.1 19.1 81.1 123.3 872.2 1662.1 245.4
Louisiana 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7
Maine 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9
Maryland 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5
Massachusetts 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1
Michigan 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5
Minnesota 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1
Mississippi 14.3 19.6 65.7 189.1 915.6 1239.9 144.4
Missouri 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4
Montana 5.4 16.7 39.2 156.8 804.9 2773.2 309.2
Nebraska 3.9 18.1 64.7 112.7 760.0 2316.1 249.1
Nevada 15.8 49.1 323.1 355.0 2453.1 4212.6 559.2
New Hampshire 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4
New Jersey 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5
New Mexico 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5
New York 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8
North Carolina 10.6 17.0 61.3 318.3 1154.1 2037.8 192.1
North Dakota 0.9 9.0 13.3 43.8 446.1 1843.0 144.7
Ohio 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4
Oklahoma 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8
Oregon 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9
Pennsylvania 5.6 19.0 130.3 128.0 877.5 1624.1 333.2
Rhode Island 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4
South Carolina 11.9 33.0 105.9 485.3 1613.6 2342.4 245.1
South Dakota 2.0 13.5 17.9 155.7 570.5 1704.4 147.5
Tennessee 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0
Texas 13.3 33.8 152.4 208.2 1603.1 2988.7 397.6
Utah 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5
Vermont 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2
Virginia 9.0 23.3 92.1 165.7 986.2 2521.2 226.7
Washington 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3
West Virginia 6.0 13.2 42.2 90.9 597.4 1341.7 163.3
Wisconsin 2.8 12.9 52.2 63.7 846.9 2614.2 220.7
Wyoming 5.4 21.9 39.7 173.9 811.6 2772.2 282.0
;
proc princomp n=7 out=out2 std;
var Murder Rape Robbery Assault Burglary Larceny Auto_Theft;
run;
proc print data=out2;
var prin1-prin7;
title 'the princomp score';
run;
proc sort data=out2;
by prin1;
run;
proc print; id State;
var prin1 Murder Rape Robbery Assault Burglary Larceny Auto_Theft;
title'Analyze for prim1';
run;
proc sort data=out2;
by prin2;
run;
proc print; id State;
var prin1 Murder Rape Robbery Assault Burglary Larceny Auto_Theft;
title'Analyze for prim2';
run;
proc sort data=out2;
by prin3;
run;
proc print; id State;
var prin1 Murder Rape Robbery Assault Burglary Larceny Auto_Theft;
title'Analyze for prim3';
run;
运行结果:
The PRINCOMP Procedure
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 4.17447791 3.14123234 0.5964 0.5964
2 1.03324557 0.26223200 0.1476 0.7440
3 0.77101357 0.33360488 0.1101 0.8541
4 0.43740869 0.14717582 0.0625 0.9166
5 0.29023287 0.13822385 0.0415 0.9581
6 0.15200902 0.01039665 0.0217 0.9798
7 0.14161237 0.0202 1.0000
Eigenvectors
Prin1 Prin2 Prin3 Prin4 Prin5 Prin6 Prin7
Murder 0.260133 0.734753 0.120318 0.559038 0.122760 0.179112 0.135343
Rape 0.424312 0.156964 -.368719 -.108216 0.339878 -.630794 -.366386
Robbery 0.401405 0.157117 0.377924 -.227353 -.736380 -.277872 0.014299
Assault 0.409892 0.163223 -.241007 -.621543 0.169257 0.436024 0.377068
Burglary 0.435312 -.282326 -.091181 0.201380 -.142232 0.525389 -.621019
Larceny 0.367286 -.459151 -.322033 0.443881 -.132102 -.151337 0.559636
Auto_Theft 0.314256 -.306014 0.732557 -.013284 0.510715 -.061246 0.078752
结果分析:从上面可以看出,前三个主成分累计方差贡献率达0.8541>85%,故可将前三个主成分看作对犯罪有显著联系;回归方程为:
Prin1=0.260133Murder+0.424312Rape+0.401405Robbery+0.409892Assault+0.435312Burglary+0.367286Larceny+0.314256Auto_Theft;
Prin2=0.734753Murder+0.156964Rape+0.157117Robbery+0.163223Assault-.282326Burglar-.459151Larceny-.306014Auto_Theft;
prin3=0.120318Murder-.368719Rape+0.377924Robbery-.241007Assault -.091181Burglary -.322033Larceny+0.732557Auto_Theft
另外,我们还可以得出分别以第一,二三主成分排名的州.以下给出以第一主成分得分排名的州:
Analyze for prim1 14:38 Tuesday, April 6, 2004 27
Auto_
State Prin1 Murder Rape Robbery Assault Burglary Larceny Theft
North Carolin . . 10.6 17.0 61.3 318.3 1154.1 2037.8
South Carolin . . 11.9 33.0 105.9 485.3 1613.6 2342.4
North Dakota -1.89517 0.9 9.0 13.3 43.8 446.1 1843.0 144.7
West Virginia -1.51788 6.0 13.2 42.2 90.9 597.4 1341.7 163.3
South Dakota -1.49205 2.0 13.5 17.9 155.7 570.5 1704.4 147.5
Iowa -1.21434 2.3 10.6 41.2 89.8 812.5 2685.1 219.9
Wisconsin -1.18654 2.8 12.9 52.2 63.7 846.9 2614.2 220.7
New Hampshire -1.16657 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4
Nebraska -1.01051 3.9 18.1 64.7 112.7 760.0 2316.1 249.1
Vermont -0.96299 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2
Maine 2 -0.89910 0.4 13.5 38.7 170.0 1253.1 2350.7 246.9
Kentucky -0.83905 10.1 19.1 81.1 123.3 872.2 1662.1 245.4
Idaho 5 -0.82026 0.5 19.4 39.6 172.5 1050.8 2599.6 237.6
Pennsylvania -0.80703 5.6 19.0 130.3 128.0 877.5 1624.1 333.2
Montana -0.76734 5.4 16.7 39.2 156.8 804.9 2773.2 309.2
Mississippi -0.74597 14.3 19.6 65.7 189.1 915.6 1239.9 144.4
Minnesota -0.71876 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1
Wyoming -0.64825 5.4 21.9 39.7 173.9 811.6 2772.2 282.0
Arkansas -0.49198 8.8 27.6 83.2 203.4 972.6 1862.1 183.4
Utah -0.46134 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5
Virginia -0.42751 9.0 23.3 92.1 165.7 986.2 2521.2 226.7
Alabama 1 -0.33484 4.2 25.2 96.8 278.3 1135.5 1881.9 280.7
Kansas -0.27429 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3
Indiana -0.21458 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4
Connecticut -0.21088 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2
Oklahoma -0.12864 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8
Georgia 1 -0.06605 1.7 31.1 140.5 256.5 1351.1 2170.2 297.9
Tennessee -0.04948 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0
State Prin1 Murder Rape Robbery Assault Burglary Larceny Theft
Rhode Island -0.01400 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4
Ohio 0.15077 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4
New Jersey 0.15878 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5
Illinois 0.29008 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6
Missouri 0.30433 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4
Texas 1 0.36099 3.3 33.8 152.4 208.2 1603.1 2988.7 397.6
Hawaii 0.41446 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4
Washington 0.50856 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3
Delaware 0.52107 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0
Louisiana 0.57120 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7
Massachusetts 0.57978 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1
New Mexico 0.64693 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5
Oregon 0.77441 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9
Maryland 1.13796 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5
Michigan 1.15746 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5
Alaska 1.23110 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3
Florida 1 1.26752 0.2 39.6 187.9 449.1 1859.9 3840.5 351.4
Colorado 1.28749 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1
Arizona 1.52164 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5
New York 1.74513 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8
California 2.14205 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
Nevada 2.59368 15.8 49.1 323.1 355.0 2453.1 4212.6 559.2
由于 North Carolin 和South Carolin缺失Murder数据,故无法进行排名,可以认为这两个州犯罪情况不严重,除去这两个州,我们可以得出North Dakota州的犯罪情况较轻(以第一主成分得分排名)
由于版面问题,第二,三主成分得分排名不在此列出,LZ可以运行程序得出结果!